相对整体维数有限的扩张

郭述锋

数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 191-200.

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数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 191-200. DOI: 10.12386/A2019sxxb0016
论文

相对整体维数有限的扩张

    郭述锋1,2
作者信息 +

Extensions with Finite Relative Global Dimension

    Shu Feng GUO1,2
Author information +
文章历史 +

摘要

代数的扩张是指两个代数之间保持单位元的同态映射.设fBA是代数的扩张,扩张f的相对整体维数是指所有A-模的相对投射维数的上确界.我们给出了扩张的相对整体维数有限的一个充分必要条件,作为应用,还获得了Hochschild的文[Relative homological algebra,Trans.Am.Math.Soc.,1956,82:246–269]中一个结果的简洁证明.

Abstract

An extension of algebras is a homomorphism of algebras preserving identities. The relative global dimension of an extension f:BA is defined to be the supremum of relative projective dimensions of all A-modules. We give a necessary and sufficient condition for an extension of algebras to have finite relative global dimension. As an application, we give a new short proof for a result in Hochschild [Relative homological algebra,Trans. Am. Math. Soc., 1956, 82: 246–269].

关键词

相对投射模 / 相对投射维数 / 相对整体维数

Key words

relatively projective module / relative projective dimension / relative global dimension

引用本文

导出引用
郭述锋. 相对整体维数有限的扩张. 数学学报, 2019, 62(2): 191-200 https://doi.org/10.12386/A2019sxxb0016
Shu Feng GUO. Extensions with Finite Relative Global Dimension. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 191-200 https://doi.org/10.12386/A2019sxxb0016

参考文献

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基金

国家自然科学基金资助项目(11331006);广西自然科学基金项目(2018GXNSFAA138191);桂林航天工业学院博士基金项目(20180601-20200601)

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